Seventy independent messages are sent from an electronic transmission center.Messages are processed sequentially, one after another. Transmission time of eachmessage is Exponential with parameterλ = 10(min^(-1)). Find the probability that all 70 messages are transmitted in less than 6minutes. (Round your answer to 4 decimal places)Required: Use the Central Limit Theorem and use Standard Normal Distribution Table

In the field of electronic communication, it is essential to ensure that messages are transmitted…

Answered: Seventy independent messages are sent…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Today, the waves are crashing onto the beach every 4.9 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.9 seconds. Round to 4 decimal places where possible. The mean of this distribution is The standard deviation is The probability that wave will crash onto the beach exactly 0.6 seconds after the person arrives is P(x = 0.6) =
Assume that adults have IQ scores that are normally distributed a mean of adult has an IQ less than 132 mu = 105 and a standard deviation sigma = 15 . Find the probability that a randomly selected adult has an IQ less than 132 the probability that a randomly selected adult has an IQ less than 132 is (type an integer or decimal rounded to four decimal places as needed)
Central Limit Theorem: When the maximum SAT score was 2400, scores had a mean = 1518 and standard deviation = 325. Assuming the scores are normally distributed, determine the probability of a score exceeding 1600. If 81 SAT scores are randomly selected, find the probability that their mean score exceeds 1600.
Today, the waves are crashing onto the beach every 5 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5 seconds. Round to 4 decimal places where possible. The mean of this distribution is The standard deviation is The probability that wave will crash onto the beach exactly 2 seconds after the person arrives is P(x = 2) = The probability that the wave will crash onto the beach between 0.4 and 2.9 seconds after the person arrives is P(0.4 < x < 2.9) = The probability that it will take longer than 1.5 seconds for the wave to crash onto the beach after the person arrives is P(x &gt 1.5) = Suppose that the person has already been standing at the shoreline for 1.3 seconds without a wave crashing in. Find the probability that it will take between 2.7 and 4.8 seconds for the wave to crash onto the shoreline. 27% of the time a person will wait at least how long before the wave crashes in?…
Today, the waves are crashing onto the beach every 6 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 6 seconds. Round to 4 decimal places where possible. The mean of this distribution is The standard deviation is The probability that wave will crash onto the beach exactly 3.9 seconds after the person arrives is P(x = 3.9) =
The amounts of sugar in a serving of children's breakfast cereals is normally distributed with a mean of 8.4 grams and a standard deviation of 2.1 grams. For a sample of 15 children's breakfast cereals, what is the probability that the sample mean amount of sugar in a serving for the 15 cereals will be at least than 10 grams? Show how you calculated your result here (type in what you typed on your calculator or computer, the function used on the calculator/computer with value input, etc) Calculation: ___________ Now type in your final simplified or rounded answer, if necessary round your answer to four decimal places. P(x¯<10 grams) = ___________
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0 degrees * C and a standard deviation of 1.00 degrees * C . A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than - 1.388 degrees * C . If this can be done on the calculator, please explain.
The life X (in hours) of a battery in constant use is a random variable with exponential density. What is the probability that the battery will last more than 12 hours (h) if the average life is 8 h?
Assume that blood pressure readings are normally distributed with a mean of 116 and a standard deviation of 8. If 100 people are randomly selected, find the probability that their mean blood pressure will be less than 118. Round to four decimal places.
In 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more than 9090 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life (150,000150,000 miles of driving) of the vehicle. NOX ++ NMOG emissions over the useful life for one car model vary Normally with mean 8484 mg/mi and standard deviation 66 mg/mi. (a) What is the probability that a single car of this model emits more than 9090 mg/mi of NOX ++ NMOG? (Enter your answer rounded to four decimal places.) (b) A company has 1616 cars of this model in its fleet. What is the probability that the average NOX ++ NMOG level ?¯x¯ of these cars is above 9090 mg/mi? (Enter your answer rounded to four decimal places.)
The migratory habits of zebra in the savanna are normally distributed with a mean of 238 days and a standard deviation of 13 days. Find the probability a single zebra will migrate in less than 220 days.
Q7) The length of time, in seconds, that a computer user takes to read his or her e- mail is distributed as lognormal random variable with μ = 1.8 and o² = 4. (a) (b) What is the probability that a user reads e-mail for more than 20 seconds? More than a minute? What is the probability that a user reads e-mail for a length of time that is equal to the mean of the underlying lognormal distribution?

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